Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(289,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.l (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(-1.73040 - 0.0755709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.289 |
Dual form | 756.2.l.b.361.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.967857 | −0.432839 | −0.216419 | − | 0.976300i | \(-0.569438\pi\) | ||||
−0.216419 | + | 0.976300i | \(0.569438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.11482 | + | 2.39941i | −0.421363 | + | 0.906892i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.728244 | −0.219574 | −0.109787 | − | 0.993955i | \(-0.535017\pi\) | ||||
−0.109787 | + | 0.993955i | \(0.535017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.81066 | + | 3.13615i | 0.502187 | + | 0.869813i | 0.999997 | + | 0.00252677i | \(0.000804296\pi\) |
−0.497810 | + | 0.867286i | \(0.665862\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.49948 | − | 6.06128i | −0.848749 | − | 1.47008i | −0.882325 | − | 0.470641i | \(-0.844023\pi\) |
0.0335755 | − | 0.999436i | \(-0.489311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.348050 | + | 0.602841i | −0.0798483 | + | 0.138301i | −0.903184 | − | 0.429253i | \(-0.858777\pi\) |
0.823336 | + | 0.567554i | \(0.192110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.43796 | −1.34241 | −0.671204 | − | 0.741273i | \(-0.734222\pi\) | ||||
−0.671204 | + | 0.741273i | \(0.734222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.06325 | −0.812650 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.34727 | + | 5.79764i | −0.621573 | + | 1.07660i | 0.367620 | + | 0.929976i | \(0.380173\pi\) |
−0.989193 | + | 0.146619i | \(0.953161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58310 | + | 7.93816i | −0.823149 | + | 1.42574i | 0.0801762 | + | 0.996781i | \(0.474452\pi\) |
−0.903326 | + | 0.428956i | \(0.858882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.07899 | − | 2.32229i | 0.182382 | − | 0.392538i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.854506 | − | 1.48005i | 0.140480 | − | 0.243318i | −0.787197 | − | 0.616701i | \(-0.788469\pi\) |
0.927677 | + | 0.373383i | \(0.121802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.62444 | + | 6.27771i | 0.566042 | + | 0.980413i | 0.996952 | + | 0.0780185i | \(0.0248593\pi\) |
−0.430910 | + | 0.902395i | \(0.641807\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.348050 | + | 0.602841i | −0.0530772 | + | 0.0919324i | −0.891343 | − | 0.453329i | \(-0.850236\pi\) |
0.838266 | + | 0.545261i | \(0.183570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.83120 | + | 6.63583i | 0.558838 | + | 0.967936i | 0.997594 | + | 0.0693294i | \(0.0220860\pi\) |
−0.438756 | + | 0.898606i | \(0.644581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.51435 | − | 5.34983i | −0.644907 | − | 0.764261i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.05637 | − | 3.56174i | −0.282465 | − | 0.489243i | 0.689527 | − | 0.724260i | \(-0.257819\pi\) |
−0.971991 | + | 0.235017i | \(0.924485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.704836 | 0.0950401 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.38809 | + | 4.13629i | −0.310903 | + | 0.538500i | −0.978558 | − | 0.205971i | \(-0.933965\pi\) |
0.667655 | + | 0.744471i | \(0.267298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46287 | − | 4.26582i | −0.315338 | − | 0.546182i | 0.664171 | − | 0.747581i | \(-0.268785\pi\) |
−0.979509 | + | 0.201399i | \(0.935451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.75246 | − | 3.03535i | −0.217366 | − | 0.376489i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.91035 | − | 5.04087i | 0.355556 | − | 0.615841i | −0.631657 | − | 0.775248i | \(-0.717625\pi\) |
0.987213 | + | 0.159407i | \(0.0509583\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.304424 | −0.0361285 | −0.0180642 | − | 0.999837i | \(-0.505750\pi\) | ||||
−0.0180642 | + | 0.999837i | \(0.505750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.33879 | + | 9.24705i | 0.624858 | + | 1.08229i | 0.988568 | + | 0.150773i | \(0.0481763\pi\) |
−0.363711 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.811862 | − | 1.74736i | 0.0925202 | − | 0.199130i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61945 | + | 2.80497i | 0.182203 | + | 0.315584i | 0.942630 | − | 0.333839i | \(-0.108344\pi\) |
−0.760428 | + | 0.649423i | \(0.775011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.618759 | + | 1.07172i | −0.0679176 | + | 0.117637i | −0.897985 | − | 0.440027i | \(-0.854969\pi\) |
0.830067 | + | 0.557664i | \(0.188302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.38700 | + | 5.86646i | 0.367372 | + | 0.636307i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.78679 | − | 10.0230i | 0.613399 | − | 1.06244i | −0.377264 | − | 0.926106i | \(-0.623135\pi\) |
0.990663 | − | 0.136333i | \(-0.0435316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.54349 | + | 0.848265i | −1.00043 | + | 0.0889223i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.336863 | − | 0.583464i | 0.0345614 | − | 0.0598622i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.32933 | − | 2.30247i | 0.134973 | − | 0.233780i | −0.790614 | − | 0.612315i | \(-0.790238\pi\) |
0.925587 | + | 0.378534i | \(0.123572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61394 | −0.160593 | −0.0802964 | − | 0.996771i | \(-0.525587\pi\) | ||||
−0.0802964 | + | 0.996771i | \(0.525587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8401 | 1.06811 | 0.534055 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534055 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.97630 | + | 8.61920i | −0.481077 | + | 0.833249i | −0.999764 | − | 0.0217146i | \(-0.993087\pi\) |
0.518688 | + | 0.854964i | \(0.326421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.27835 | − | 16.0706i | −0.888705 | − | 1.53928i | −0.841407 | − | 0.540401i | \(-0.818272\pi\) |
−0.0472974 | − | 0.998881i | \(-0.515061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.75824 | − | 9.97356i | −0.541689 | − | 0.938234i | −0.998807 | − | 0.0488275i | \(-0.984452\pi\) |
0.457118 | − | 0.889406i | \(-0.348882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.23103 | 0.581046 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.4448 | − | 1.63945i | 1.69083 | − | 0.150288i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4697 | −0.951787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.77193 | 0.784586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.06977 | 0.804812 | 0.402406 | − | 0.915461i | \(-0.368174\pi\) | ||||
0.402406 | + | 0.915461i | \(0.368174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0851 | −1.14325 | −0.571625 | − | 0.820515i | \(-0.693687\pi\) | ||||
−0.571625 | + | 0.820515i | \(0.693687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.05845 | − | 1.50718i | −0.0917792 | − | 0.130689i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0764 | 1.71525 | 0.857623 | − | 0.514279i | \(-0.171940\pi\) | ||||
0.857623 | + | 0.514279i | \(0.171940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.337832 | + | 0.585143i | 0.0286546 | + | 0.0496312i | 0.879997 | − | 0.474979i | \(-0.157544\pi\) |
−0.851343 | + | 0.524610i | \(0.824211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.31860 | − | 2.28388i | −0.110267 | − | 0.190988i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.23968 | − | 5.61129i | 0.269041 | − | 0.465992i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5088 | −1.76207 | −0.881034 | − | 0.473054i | \(-0.843152\pi\) | ||||
−0.881034 | + | 0.473054i | \(0.843152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1705 | 1.15318 | 0.576588 | − | 0.817035i | \(-0.304384\pi\) | ||||
0.576588 | + | 0.817035i | \(0.304384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.43579 | − | 7.68301i | 0.356291 | − | 0.617114i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.99845 | − | 13.8537i | 0.638346 | − | 1.10565i | −0.347450 | − | 0.937699i | \(-0.612952\pi\) |
0.985796 | − | 0.167949i | \(-0.0537143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.17717 | − | 15.4473i | 0.565641 | − | 1.21742i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0904 | + | 17.4771i | −0.790340 | + | 1.36891i | 0.135417 | + | 0.990789i | \(0.456763\pi\) |
−0.925757 | + | 0.378120i | \(0.876571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2299 | + | 21.1828i | 0.946378 | + | 1.63917i | 0.752968 | + | 0.658057i | \(0.228621\pi\) |
0.193410 | + | 0.981118i | \(0.438045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0569772 | + | 0.0986874i | −0.00438286 | + | 0.00759134i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.87800 | + | 17.1092i | 0.751010 | + | 1.30079i | 0.947333 | + | 0.320249i | \(0.103767\pi\) |
−0.196323 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.52980 | − | 9.74941i | 0.342421 | − | 0.736986i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.32439 | + | 10.9542i | 0.472707 | + | 0.818753i | 0.999512 | − | 0.0312332i | \(-0.00994346\pi\) |
−0.526805 | + | 0.849986i | \(0.676610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5654 | 0.933975 | 0.466988 | − | 0.884264i | \(-0.345339\pi\) | ||||
0.466988 | + | 0.884264i | \(0.345339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.827040 | + | 1.43248i | −0.0608052 | + | 0.105318i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.54848 | + | 4.41409i | 0.186363 | + | 0.322790i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.70316 | − | 6.41407i | −0.267951 | − | 0.464105i | 0.700381 | − | 0.713769i | \(-0.253013\pi\) |
−0.968333 | + | 0.249663i | \(0.919680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.813937 | − | 1.40978i | 0.0585885 | − | 0.101478i | −0.835244 | − | 0.549880i | \(-0.814673\pi\) |
0.893832 | + | 0.448402i | \(0.148007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.27125 | 0.589302 | 0.294651 | − | 0.955605i | \(-0.404797\pi\) | ||||
0.294651 | + | 0.955605i | \(0.404797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.34411 | + | 9.25627i | 0.378834 | + | 0.656159i | 0.990893 | − | 0.134653i | \(-0.0429919\pi\) |
−0.612059 | + | 0.790812i | \(0.709659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.1793 | − | 14.4948i | −0.714448 | − | 1.01734i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50794 | − | 6.07593i | −0.245005 | − | 0.424361i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.253466 | − | 0.439015i | 0.0175326 | − | 0.0303673i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2725 | − | 19.5246i | −0.776034 | − | 1.34413i | −0.934211 | − | 0.356720i | \(-0.883895\pi\) |
0.158178 | − | 0.987411i | \(-0.449438\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.336863 | − | 0.583464i | 0.0229739 | − | 0.0397919i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.9376 | − | 19.8464i | −0.946145 | − | 1.34726i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6727 | − | 21.9498i | 0.852461 | − | 1.47651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.70093 | − | 6.41020i | 0.247832 | − | 0.429258i | −0.715092 | − | 0.699031i | \(-0.753615\pi\) |
0.962924 | + | 0.269772i | \(0.0869484\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.598173 | 0.0397021 | 0.0198511 | − | 0.999803i | \(-0.493681\pi\) | ||||
0.0198511 | + | 0.999803i | \(0.493681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.03717 | −0.266783 | −0.133392 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133392 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.59754 | − | 9.69523i | 0.366707 | − | 0.635155i | −0.622341 | − | 0.782746i | \(-0.713818\pi\) |
0.989049 | + | 0.147591i | \(0.0471518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.70805 | − | 6.42254i | −0.241887 | − | 0.418960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8171 | + | 22.1999i | 0.829069 | + | 1.43599i | 0.898769 | + | 0.438421i | \(0.144462\pi\) |
−0.0697006 | + | 0.997568i | \(0.522204\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.59180 | −0.424615 | −0.212307 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212307 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.36924 | + | 5.17787i | 0.279141 | + | 0.330802i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.52080 | −0.160395 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.0438 | −1.58075 | −0.790374 | − | 0.612624i | \(-0.790114\pi\) | ||||
−0.790374 | + | 0.612624i | \(0.790114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.68840 | 0.294757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1407 | 1.13159 | 0.565794 | − | 0.824547i | \(-0.308570\pi\) | ||||
0.565794 | + | 0.824547i | \(0.308570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.59862 | + | 3.70030i | 0.161471 | + | 0.229926i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8088 | −0.789822 | −0.394911 | − | 0.918719i | \(-0.629225\pi\) | ||||
−0.394911 | + | 0.918719i | \(0.629225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.99028 | + | 3.44726i | 0.122262 | + | 0.211763i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4412 | + | 25.0129i | 0.880497 | + | 1.52507i | 0.850789 | + | 0.525507i | \(0.176124\pi\) |
0.0297079 | + | 0.999559i | \(0.490542\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.59579 | − | 7.96015i | 0.279175 | − | 0.483544i | −0.692005 | − | 0.721892i | \(-0.743273\pi\) |
0.971180 | + | 0.238348i | \(0.0766059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.95904 | 0.178437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.91557 | −0.235264 | −0.117632 | − | 0.993057i | \(-0.537530\pi\) | ||||
−0.117632 | + | 0.993057i | \(0.537530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.64654 | + | 13.2442i | −0.456154 | + | 0.790082i | −0.998754 | − | 0.0499093i | \(-0.984107\pi\) |
0.542600 | + | 0.839991i | \(0.317440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4890 | + | 21.6315i | −0.742392 | + | 1.28586i | 0.209011 | + | 0.977913i | \(0.432975\pi\) |
−0.951403 | + | 0.307947i | \(0.900358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.1034 | + | 1.69799i | −1.12764 | + | 0.100229i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9928 | + | 27.7003i | −0.940751 | + | 1.62943i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.08092 | + | 7.06835i | 0.238410 | + | 0.412938i | 0.960258 | − | 0.279114i | \(-0.0900406\pi\) |
−0.721848 | + | 0.692051i | \(0.756707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.31133 | − | 4.00334i | 0.134571 | − | 0.233084i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.6570 | − | 20.1904i | −0.674139 | − | 1.16764i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05845 | − | 1.50718i | −0.0610080 | − | 0.0868722i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.38371 | + | 4.12870i | 0.136491 | + | 0.236409i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0692 | 1.03126 | 0.515631 | − | 0.856811i | \(-0.327558\pi\) | ||||
0.515631 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.00384 | + | 8.66691i | −0.283742 | + | 0.491456i | −0.972303 | − | 0.233723i | \(-0.924909\pi\) |
0.688561 | + | 0.725178i | \(0.258243\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.49532 | − | 2.58998i | −0.0845207 | − | 0.146394i | 0.820666 | − | 0.571408i | \(-0.193603\pi\) |
−0.905187 | + | 0.425014i | \(0.860269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.9246 | − | 20.6541i | −0.669754 | − | 1.16005i | −0.977973 | − | 0.208732i | \(-0.933066\pi\) |
0.308219 | − | 0.951315i | \(-0.400267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.43763 | − | 4.22210i | 0.136481 | − | 0.236392i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.87199 | 0.271085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.35717 | − | 12.7430i | −0.408102 | − | 0.706854i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.1932 | + | 1.79486i | −1.11329 | + | 0.0989536i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.01886 | + | 13.8891i | 0.440757 | + | 0.763413i | 0.997746 | − | 0.0671069i | \(-0.0213768\pi\) |
−0.556989 | + | 0.830520i | \(0.688044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.81680 | + | 4.87884i | −0.153898 | + | 0.266560i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8985 | + | 29.2691i | 0.920520 | + | 1.59439i | 0.798613 | + | 0.601845i | \(0.205568\pi\) |
0.121907 | + | 0.992542i | \(0.461099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.33761 | − | 5.78092i | 0.180742 | − | 0.313054i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8691 | − | 4.86767i | 0.964842 | − | 0.262829i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.6637 | − | 30.5944i | 0.948237 | − | 1.64240i | 0.199102 | − | 0.979979i | \(-0.436198\pi\) |
0.749136 | − | 0.662417i | \(-0.230469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.75344 | + | 9.96526i | −0.307975 | + | 0.533428i | −0.977919 | − | 0.208983i | \(-0.932985\pi\) |
0.669944 | + | 0.742411i | \(0.266318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.8863 | −1.32457 | −0.662283 | − | 0.749254i | \(-0.730412\pi\) | ||||
−0.662283 | + | 0.749254i | \(0.730412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.294639 | 0.0156378 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.22681 | + | 15.9813i | −0.486972 | + | 0.843461i | −0.999888 | − | 0.0149785i | \(-0.995232\pi\) |
0.512916 | + | 0.858439i | \(0.328565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.25772 | + | 16.0348i | 0.487249 | + | 0.843939i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.16718 | − | 8.94982i | −0.270463 | − | 0.468455i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.2138 | −0.950750 | −0.475375 | − | 0.879783i | \(-0.657688\pi\) | ||||
−0.475375 | + | 0.879783i | \(0.657688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8386 | − | 0.963378i | 0.562711 | − | 0.0500161i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1999 | −0.942355 | −0.471177 | − | 0.882038i | \(-0.656171\pi\) | ||||
−0.471177 | + | 0.882038i | \(0.656171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.2431 | −1.24858 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.1061 | −1.23825 | −0.619124 | − | 0.785293i | \(-0.712512\pi\) | ||||
−0.619124 | + | 0.785293i | \(0.712512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.43694 | 0.328912 | 0.164456 | − | 0.986384i | \(-0.447413\pi\) | ||||
0.164456 | + | 0.986384i | \(0.447413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.785766 | + | 1.69119i | −0.0400463 | + | 0.0861911i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.8597 | −1.71676 | −0.858379 | − | 0.513017i | \(-0.828528\pi\) | ||||
−0.858379 | + | 0.513017i | \(0.828528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5295 | + | 39.0223i | 1.13937 | + | 1.97344i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.56740 | − | 2.71481i | −0.0788643 | − | 0.136597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.808630 | + | 1.40059i | −0.0405840 | + | 0.0702935i | −0.885604 | − | 0.464441i | \(-0.846255\pi\) |
0.845020 | + | 0.534735i | \(0.179588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.75382 | −0.287332 | −0.143666 | − | 0.989626i | \(-0.545889\pi\) | ||||
−0.143666 | + | 0.989626i | \(0.545889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.1937 | −1.65350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.622289 | + | 1.07784i | −0.0308457 | + | 0.0534263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.88631 | − | 4.99923i | 0.142719 | − | 0.247196i | −0.785801 | − | 0.618480i | \(-0.787749\pi\) |
0.928520 | + | 0.371284i | \(0.121082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.26237 | − | 10.3412i | −0.357358 | − | 0.508859i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.598871 | − | 1.03727i | 0.0293974 | − | 0.0509178i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.29032 | + | 16.0913i | 0.453862 | + | 0.786111i | 0.998622 | − | 0.0524804i | \(-0.0167127\pi\) |
−0.544760 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.05788 | + | 13.9567i | −0.392717 | + | 0.680206i | −0.992807 | − | 0.119727i | \(-0.961798\pi\) |
0.600090 | + | 0.799933i | \(0.295131\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.2193 | + | 24.6285i | 0.689737 | + | 1.19466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9811 | − | 1.15382i | 0.628200 | − | 0.0558371i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.82664 | − | 3.16383i | −0.0879860 | − | 0.152396i | 0.818674 | − | 0.574259i | \(-0.194710\pi\) |
−0.906660 | + | 0.421863i | \(0.861376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6697 | 0.608865 | 0.304432 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304432 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.24073 | − | 3.88107i | 0.107189 | − | 0.185657i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.85810 | − | 10.1465i | −0.279592 | − | 0.484267i | 0.691692 | − | 0.722193i | \(-0.256866\pi\) |
−0.971283 | + | 0.237926i | \(0.923532\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.8735 | − | 25.7617i | −0.706661 | − | 1.22397i | −0.966089 | − | 0.258210i | \(-0.916867\pi\) |
0.259428 | − | 0.965763i | \(-0.416466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.60079 | + | 9.70085i | −0.265503 | + | 0.459865i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.0193 | −0.520034 | −0.260017 | − | 0.965604i | \(-0.583728\pi\) | ||||
−0.260017 | + | 0.965604i | \(0.583728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.63947 | − | 4.57170i | −0.124288 | − | 0.215273i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.23673 | − | 0.820999i | 0.433025 | − | 0.0384890i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.258224 | − | 0.447257i | −0.0120792 | − | 0.0209218i | 0.859923 | − | 0.510424i | \(-0.170512\pi\) |
−0.872002 | + | 0.489503i | \(0.837178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.54962 | − | 6.14813i | 0.165322 | − | 0.286347i | −0.771447 | − | 0.636293i | \(-0.780467\pi\) |
0.936770 | + | 0.349946i | \(0.113800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.91148 | − | 8.50693i | −0.228256 | − | 0.395351i | 0.729035 | − | 0.684476i | \(-0.239969\pi\) |
−0.957291 | + | 0.289125i | \(0.906636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.79604 | − | 8.30698i | 0.221934 | − | 0.384401i | −0.733461 | − | 0.679731i | \(-0.762096\pi\) |
0.955395 | + | 0.295330i | \(0.0954297\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.85061 | + | 12.6028i | 0.408683 | + | 0.581943i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.253466 | − | 0.439015i | 0.0116544 | − | 0.0201859i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41422 | − | 2.44950i | 0.0648887 | − | 0.112391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.2724 | −0.743506 | −0.371753 | − | 0.928332i | \(-0.621243\pi\) | ||||
−0.371753 | + | 0.928332i | \(0.621243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.18888 | 0.282189 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.28660 | + | 2.22846i | −0.0584217 | + | 0.101189i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.50511 | − | 16.4633i | −0.430718 | − | 0.746025i | 0.566217 | − | 0.824256i | \(-0.308406\pi\) |
−0.996935 | + | 0.0782307i | \(0.975073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.55413 | − | 4.42387i | −0.115266 | − | 0.199647i | 0.802620 | − | 0.596491i | \(-0.203439\pi\) |
−0.917886 | + | 0.396844i | \(0.870105\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.8549 | 2.11024 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.339378 | − | 0.730439i | 0.0152232 | − | 0.0327646i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5276 | −1.27707 | −0.638536 | − | 0.769592i | \(-0.720459\pi\) | ||||
−0.638536 | + | 0.769592i | \(0.720459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.05885 | −0.180975 | −0.0904877 | − | 0.995898i | \(-0.528843\pi\) | ||||
−0.0904877 | + | 0.995898i | \(0.528843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.56206 | 0.0695108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.2605 | −0.765056 | −0.382528 | − | 0.923944i | \(-0.624946\pi\) | ||||
−0.382528 | + | 0.923944i | \(0.624946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1393 | + | 2.50114i | −1.24481 | + | 0.110644i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.4917 | −0.462320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.79005 | − | 4.83250i | −0.122706 | − | 0.212533i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0525 | + | 29.5358i | 0.747083 | + | 1.29399i | 0.949215 | + | 0.314628i | \(0.101880\pi\) |
−0.202132 | + | 0.979358i | \(0.564787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.44847 | + | 16.3652i | −0.413153 | + | 0.715602i | −0.995233 | − | 0.0975299i | \(-0.968906\pi\) |
0.582080 | + | 0.813132i | \(0.302239\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 64.1539 | 2.79459 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4473 | 0.802057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.1252 | + | 22.7336i | −0.568517 | + | 0.984701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.81634 | − | 8.34215i | 0.208229 | − | 0.360663i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.28754 | + | 3.89598i | 0.141605 | + | 0.167812i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.564117 | − | 0.977080i | 0.0242533 | − | 0.0420080i | −0.853644 | − | 0.520857i | \(-0.825613\pi\) |
0.877897 | + | 0.478849i | \(0.158946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.98012 | + | 15.5540i | 0.384666 | + | 0.666261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8427 | − | 27.4404i | 0.677386 | − | 1.17327i | −0.298380 | − | 0.954447i | \(-0.596446\pi\) |
0.975765 | − | 0.218819i | \(-0.0702205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.33004 | − | 4.03575i | −0.0992630 | − | 0.171929i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.53568 | + | 0.758687i | −0.362974 | + | 0.0322626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8135 | + | 23.9257i | 0.585298 | + | 1.01377i | 0.994838 | + | 0.101474i | \(0.0323559\pi\) |
−0.409540 | + | 0.912292i | \(0.634311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.52080 | −0.106619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.920685 | − | 1.59467i | 0.0388022 | − | 0.0672074i | −0.845972 | − | 0.533227i | \(-0.820979\pi\) |
0.884774 | + | 0.466020i | \(0.154312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.57315 | + | 9.65298i | 0.234464 | + | 0.406104i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.75524 | − | 9.96837i | −0.241272 | − | 0.417896i | 0.719805 | − | 0.694177i | \(-0.244231\pi\) |
−0.961077 | + | 0.276281i | \(0.910898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.35262 | − | 7.53896i | 0.182152 | − | 0.315496i | −0.760461 | − | 0.649383i | \(-0.775027\pi\) |
0.942613 | + | 0.333887i | \(0.108361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.1591 | 1.09091 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.24358 | − | 12.5462i | −0.301554 | − | 0.522307i | 0.674934 | − | 0.737878i | \(-0.264172\pi\) |
−0.976488 | + | 0.215571i | \(0.930839\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.88170 | − | 2.67944i | −0.0780659 | − | 0.111162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.49754 | + | 2.59382i | 0.0620218 | + | 0.107425i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.3695 | − | 24.8886i | 0.593091 | − | 1.02726i | −0.400722 | − | 0.916200i | \(-0.631241\pi\) |
0.993813 | − | 0.111065i | \(-0.0354261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.19030 | − | 5.52576i | −0.131454 | − | 0.227685i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.82328 | + | 11.8183i | −0.280199 | + | 0.485318i | −0.971434 | − | 0.237312i | \(-0.923734\pi\) |
0.691235 | + | 0.722630i | \(0.257067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8519 | + | 1.58676i | −0.731858 | + | 0.0650506i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.64585 | − | 4.58275i | 0.108106 | − | 0.187246i | −0.806897 | − | 0.590693i | \(-0.798855\pi\) |
0.915003 | + | 0.403447i | \(0.132188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0522 | − | 29.5353i | 0.695574 | − | 1.20477i | −0.274412 | − | 0.961612i | \(-0.588483\pi\) |
0.969987 | − | 0.243158i | \(-0.0781834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.1331 | 0.411971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.04464 | −0.367111 | −0.183555 | − | 0.983009i | \(-0.558761\pi\) | ||||
−0.183555 | + | 0.983009i | \(0.558761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8740 | + | 24.0305i | −0.561282 | + | 0.972169i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.97889 | + | 10.3557i | 0.241485 | + | 0.418264i | 0.961137 | − | 0.276070i | \(-0.0890322\pi\) |
−0.719653 | + | 0.694334i | \(0.755699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.13220 | − | 8.88923i | −0.206615 | − | 0.357867i | 0.744031 | − | 0.668145i | \(-0.232911\pi\) |
−0.950646 | + | 0.310278i | \(0.899578\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.5605 | −1.75085 | −0.875423 | − | 0.483358i | \(-0.839417\pi\) | ||||
−0.875423 | + | 0.483358i | \(0.839417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.5981 | + | 25.0588i | 0.705053 | + | 1.00396i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8263 | 0.473051 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.9613 | −0.476929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.3703 | 0.771119 | 0.385559 | − | 0.922683i | \(-0.374008\pi\) | ||||
0.385559 | + | 0.922683i | \(0.374008\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.77825 | −0.348354 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.60395 | − | 23.8444i | 0.340901 | − | 0.944750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50016 | −0.177746 | −0.0888728 | − | 0.996043i | \(-0.528326\pi\) | ||||
−0.0888728 | + | 0.996043i | \(0.528326\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9045 | − | 36.2077i | −0.824394 | − | 1.42789i | −0.902381 | − | 0.430939i | \(-0.858183\pi\) |
0.0779869 | − | 0.996954i | \(-0.475151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.9381 | − | 20.6773i | −0.469334 | − | 0.812910i | 0.530052 | − | 0.847965i | \(-0.322173\pi\) |
−0.999385 | + | 0.0350555i | \(0.988839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.73911 | − | 3.01223i | 0.0682661 | − | 0.118240i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.33347 | 0.326114 | 0.163057 | − | 0.986617i | \(-0.447865\pi\) | ||||
0.163057 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.6645 | 0.494843 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.2488 | − | 35.0719i | 0.788781 | − | 1.36621i | −0.137933 | − | 0.990442i | \(-0.544046\pi\) |
0.926714 | − | 0.375767i | \(-0.122621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88559 | − | 6.73004i | 0.151132 | − | 0.261768i | −0.780512 | − | 0.625141i | \(-0.785042\pi\) |
0.931644 | + | 0.363373i | \(0.118375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.02443 | + | 1.45873i | 0.0397256 | + | 0.0565672i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.5496 | − | 37.3250i | 0.834404 | − | 1.44523i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.79357 | + | 3.10656i | 0.0692400 | + | 0.119927i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7830 | + | 39.4614i | −0.878221 | + | 1.52112i | −0.0249302 | + | 0.999689i | \(0.507936\pi\) |
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.54521 | + | 11.3366i | 0.251553 | + | 0.435702i | 0.963954 | − | 0.266071i | \(-0.0857254\pi\) |
−0.712401 | + | 0.701773i | \(0.752392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.04261 | + | 5.75646i | 0.155141 | + | 0.220913i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6506 | + | 21.9114i | 0.484060 | + | 0.838417i | 0.999832 | − | 0.0183087i | \(-0.00582815\pi\) |
−0.515772 | + | 0.856726i | \(0.672495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.4311 | −0.742425 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.44679 | − | 12.8982i | 0.283700 | − | 0.491383i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.2016 | + | 21.1337i | 0.464170 | + | 0.803965i | 0.999164 | − | 0.0408905i | \(-0.0130195\pi\) |
−0.534994 | + | 0.844856i | \(0.679686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.326974 | − | 0.566335i | −0.0124028 | − | 0.0214823i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.3673 | − | 43.9375i | 0.960855 | − | 1.66425i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4137 | 0.695476 | 0.347738 | − | 0.937592i | \(-0.386950\pi\) | ||||
0.347738 | + | 0.937592i | \(0.386950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.594823 | + | 1.03026i | 0.0224342 | + | 0.0388571i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.79925 | − | 3.87250i | 0.0676679 | − | 0.145640i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.66501 | + | 11.5441i | 0.250310 | + | 0.433549i | 0.963611 | − | 0.267308i | \(-0.0861342\pi\) |
−0.713301 | + | 0.700858i | \(0.752801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.5058 | − | 51.1056i | 1.10500 | − | 1.91392i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.27622 | + | 2.21047i | 0.0477278 | + | 0.0826671i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.84705 | − | 13.5915i | 0.292646 | − | 0.506877i | −0.681789 | − | 0.731549i | \(-0.738798\pi\) |
0.974434 | + | 0.224672i | \(0.0721310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0848 | + | 26.0099i | −0.450062 | + | 0.968660i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.6008 | − | 23.5573i | 0.505121 | − | 0.874896i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.8388 | + | 22.2374i | −0.476163 | + | 0.824739i | −0.999627 | − | 0.0273090i | \(-0.991306\pi\) |
0.523464 | + | 0.852048i | \(0.324640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87199 | 0.180197 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.17308 | 0.0433288 | 0.0216644 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216644 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.11944 | + | 3.67098i | −0.0780707 | + | 0.135222i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6114 | + | 20.1116i | 0.427133 | + | 0.739816i | 0.996617 | − | 0.0821861i | \(-0.0261902\pi\) |
−0.569484 | + | 0.822003i | \(0.692857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.7846 | − | 20.4115i | −0.432335 | − | 0.748826i | 0.564739 | − | 0.825269i | \(-0.308977\pi\) |
−0.997074 | + | 0.0764439i | \(0.975643\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.8174 | 0.762691 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1333 | − | 21.5490i | −0.552959 | − | 0.787385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.1062 | 1.60946 | 0.804728 | − | 0.593643i | \(-0.202311\pi\) | ||||
0.804728 | + | 0.593643i | \(0.202311\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.7150 | −0.499139 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.71020 | −0.0985040 | −0.0492520 | − | 0.998786i | \(-0.515684\pi\) | ||||
−0.0492520 | + | 0.998786i | \(0.515684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.0496 | −1.05305 | −0.526524 | − | 0.850160i | \(-0.676505\pi\) | ||||
−0.526524 | + | 0.850160i | \(0.676505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.9036 | − | 4.34676i | 1.77043 | − | 0.157363i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.2961 | −0.624525 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.25175 | − | 9.09629i | −0.189383 | − | 0.328021i | 0.755662 | − | 0.654962i | \(-0.227315\pi\) |
−0.945045 | + | 0.326941i | \(0.893982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9230 | + | 20.6513i | 0.428841 | + | 0.742774i | 0.996771 | − | 0.0803029i | \(-0.0255888\pi\) |
−0.567930 | + | 0.823077i | \(0.692255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.6223 | − | 32.2548i | 0.668933 | − | 1.15863i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.04595 | −0.180790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.221695 | 0.00793287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.74136 | + | 13.4084i | −0.276301 | + | 0.478567i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.19788 | − | 3.80684i | 0.0783460 | − | 0.135699i | −0.824190 | − | 0.566313i | \(-0.808369\pi\) |
0.902536 | + | 0.430613i | \(0.141703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.3501 | − | 2.69764i | 1.07912 | − | 0.0959171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.91885 | − | 15.4479i | 0.316717 | − | 0.548571i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.56236 | + | 4.43813i | 0.0907633 | + | 0.157207i | 0.907833 | − | 0.419333i | \(-0.137736\pi\) |
−0.817069 | + | 0.576540i | \(0.804403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.8144 | − | 46.4440i | 0.948627 | − | 1.64307i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.88794 | − | 6.73410i | −0.137202 | − | 0.237641i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.94648 | + | 14.9508i | −0.244831 | + | 0.526946i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4612 | + | 28.5116i | 0.578744 | + | 1.00241i | 0.995624 | + | 0.0934519i | \(0.0297901\pi\) |
−0.416880 | + | 0.908961i | \(0.636877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.8830 | −1.11956 | −0.559781 | − | 0.828640i | \(-0.689115\pi\) | ||||
−0.559781 | + | 0.828640i | \(0.689115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.76605 | − | 16.9153i | 0.342090 | − | 0.592517i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.242278 | − | 0.419638i | −0.00847624 | − | 0.0146813i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.1139 | + | 29.6421i | 0.597278 | + | 1.03452i | 0.993221 | + | 0.116241i | \(0.0370844\pi\) |
−0.395943 | + | 0.918275i | \(0.629582\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1866 | + | 33.2321i | −0.668802 | + | 1.15840i | 0.309437 | + | 0.950920i | \(0.399859\pi\) |
−0.978239 | + | 0.207480i | \(0.933474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.23903 | −0.321273 | −0.160636 | − | 0.987014i | \(-0.551355\pi\) | ||||
−0.160636 | + | 0.987014i | \(0.551355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.8224 | + | 36.0654i | 0.723191 | + | 1.25260i | 0.959714 | + | 0.280978i | \(0.0906589\pi\) |
−0.236523 | + | 0.971626i | \(0.576008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.6289 | + | 46.0844i | −0.576159 | + | 1.59673i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.8368 | − | 20.5019i | −0.409629 | − | 0.709499i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.4241 | − | 26.7154i | 0.532500 | − | 0.922318i | −0.466780 | − | 0.884374i | \(-0.654586\pi\) |
0.999280 | − | 0.0379439i | \(-0.0120808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90845 | − | 13.6978i | −0.272705 | − | 0.472339i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0551458 | − | 0.0955153i | 0.00189707 | − | 0.00328583i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.6718 | − | 25.1210i | 0.401048 | − | 0.863168i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.50128 | + | 9.52849i | −0.188581 | + | 0.326632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4171 | + | 19.7750i | −0.390913 | + | 0.677082i | −0.992570 | − | 0.121673i | \(-0.961174\pi\) |
0.601657 | + | 0.798755i | \(0.294507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.3441 | 1.82220 | 0.911100 | − | 0.412186i | \(-0.135235\pi\) | ||||
0.911100 | + | 0.412186i | \(0.135235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1757 | −0.790743 | −0.395372 | − | 0.918521i | \(-0.629384\pi\) | ||||
−0.395372 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.58456 | + | 7.94069i | −0.156060 | + | 0.270304i | −0.933445 | − | 0.358722i | \(-0.883213\pi\) |
0.777384 | + | 0.629026i | \(0.216546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.56049 | − | 16.5593i | −0.325067 | − | 0.563032i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.17936 | − | 2.04270i | −0.0400069 | − | 0.0692940i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0786 | 0.714221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.77914 | + | 21.0475i | −0.330595 | + | 0.711535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.2380 | 1.25744 | 0.628718 | − | 0.777633i | \(-0.283580\pi\) | ||||
0.628718 | + | 0.777633i | \(0.283580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.15345 | −0.241006 | −0.120503 | − | 0.992713i | \(-0.538451\pi\) | ||||
−0.120503 | + | 0.992713i | \(0.538451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8688 | −1.34169 | −0.670846 | − | 0.741596i | \(-0.734069\pi\) | ||||
−0.670846 | + | 0.741596i | \(0.734069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3509 | 0.716893 | 0.358447 | − | 0.933550i | \(-0.383306\pi\) | ||||
0.358447 | + | 0.933550i | \(0.383306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1112 | + | 21.7621i | −0.339118 | + | 0.729878i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.33380 | −0.178489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.12111 | − | 10.6021i | −0.204606 | − | 0.354388i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.6818 | − | 53.1424i | −1.02329 | − | 1.77240i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.3925 | + | 24.9285i | −0.479483 | + | 0.830490i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.1615 | −0.404261 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6024 | −0.750499 | −0.375250 | − | 0.926924i | \(-0.622443\pi\) | ||||
−0.375250 | + | 0.926924i | \(0.622443\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.7594 | + | 22.0999i | −0.422738 | + | 0.732203i | −0.996206 | − | 0.0870243i | \(-0.972264\pi\) |
0.573468 | + | 0.819228i | \(0.305598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.450607 | − | 0.780475i | 0.0149129 | − | 0.0258300i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5876 | − | 31.3965i | 0.481723 | − | 1.03681i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.71326 | − | 9.89566i | 0.188463 | − | 0.326428i | −0.756275 | − | 0.654254i | \(-0.772983\pi\) |
0.944738 | + | 0.327826i | \(0.106316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.551208 | − | 0.954721i | −0.0181432 | − | 0.0314250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.47207 | + | 6.01381i | −0.114161 | + | 0.197733i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.79851 | + | 11.7754i | 0.223052 | + | 0.386337i | 0.955733 | − | 0.294235i | \(-0.0950648\pi\) |
−0.732681 | + | 0.680572i | \(0.761731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.79632 | − | 0.859423i | 0.157193 | − | 0.0281665i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.46656 | − | 4.27221i | −0.0806652 | − | 0.139716i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1455 | −0.364109 | −0.182054 | − | 0.983288i | \(-0.558275\pi\) | ||||
−0.182054 | + | 0.983288i | \(0.558275\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7310 | − | 35.9072i | 0.675813 | − | 1.17054i | −0.300418 | − | 0.953808i | \(-0.597126\pi\) |
0.976231 | − | 0.216734i | \(-0.0695405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3340 | − | 40.4156i | −0.759859 | − | 1.31611i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.2784 | + | 36.8552i | 0.691454 | + | 1.19763i | 0.971362 | + | 0.237606i | \(0.0763627\pi\) |
−0.279908 | + | 0.960027i | \(0.590304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3335 | + | 33.4865i | −0.627590 | + | 1.08702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.2114 | −0.687106 | −0.343553 | − | 0.939133i | \(-0.611630\pi\) | ||||
−0.343553 | + | 0.939133i | \(0.611630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58413 | + | 6.20790i | 0.115980 | + | 0.200883i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.3816 | + | 48.1716i | −0.722741 | + | 1.55554i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5096 | − | 45.9160i | −0.855150 | − | 1.48116i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.787775 | + | 1.36447i | −0.0253594 | + | 0.0439237i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.83257 | − | 17.0305i | −0.316194 | − | 0.547664i | 0.663496 | − | 0.748179i | \(-0.269072\pi\) |
−0.979691 | + | 0.200515i | \(0.935738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2892 | − | 21.2855i | 0.394379 | − | 0.683084i | −0.598643 | − | 0.801016i | \(-0.704293\pi\) |
0.993022 | + | 0.117932i | \(0.0376265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78062 | + | 0.158269i | −0.0570841 | + | 0.00507387i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.7359 | + | 41.1117i | −0.759378 | + | 1.31528i | 0.183790 | + | 0.982966i | \(0.441163\pi\) |
−0.943168 | + | 0.332316i | \(0.892170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.21420 | + | 7.29920i | −0.134686 | + | 0.233284i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5440 | −0.878516 | −0.439258 | − | 0.898361i | \(-0.644759\pi\) | ||||
−0.439258 | + | 0.898361i | \(0.644759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00539 | −0.255073 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.24073 | − | 3.88107i | 0.0712512 | − | 0.123411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2335 | + | 33.3135i | 0.610973 | + | 1.05824i | 0.991077 | + | 0.133293i | \(0.0425551\pi\) |
−0.380103 | + | 0.924944i | \(0.624112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.17233 | − | 8.95874i | −0.163974 | − | 0.284011i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.4544 | −1.02784 | −0.513921 | − | 0.857837i | \(-0.671808\pi\) | ||||
−0.513921 | + | 0.857837i | \(0.671808\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))